Teaching Least Squares in Matrix Notation

Authors

  • Guglielmo Monaco Department of Chemistry and Biology ”A. Zambelli”, University of Salerno, Italy
  • Aniello Fedullo Department of Physics "E. R. Caianiello" University of Salerno, Italy

DOI:

https://doi.org/10.23755/rm.v32i0.335

Keywords:

coefficient of determination, weighted sample mean, resampling, undergraduate education.

Abstract

Material for teaching least squares at the undergraduate level in matrix
notation is reported. The weighted least squares equations are first derived
in matrix form; equivalence with the standard results obtained by standard
algebra are then given for the weighted average and the simplest linear re-
gression. Indicators of goodness of fit are introduced and interpreted. Even-
tually a basic equation for resampling is derived.

References

R.J. Carroll and D. Ruppert. Transformation and weighting in regression. Chapmand and Hall, 1988.

G. Casella and R.L. Berger. Statistical inference. Cengage Learning, 2001.

A. J. Dobson and A. G. Barnett. An Introduction to Generalised Linear Models. Chapman and Hall, 2008.

R. W. Farebrother. Relations among subset estimators: A bibliographical note. Technometrics, 27(1):85–86, 1985.

W.H. Greene. Econometric Analysis. Prentice Hall, 2012.

J. R. Taylor. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books, 1997.

C. F. J. Wu. Jackknife, bootstrap and other resampling methods in regression analysis. The Annals of Statistics, 14(4):1261–1295, 1986.

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Published

2017-07-30

Issue

Vol. 32 (2017)

Section

Volume 32-2017

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